A Reliability Evaluation Method for Binary-Node Multi-State Networks Considering Node-Component State Dependence

Reliability evaluation of multi-state networks is fundamental to the design, operation, and optimization of complex systems. Traditional studies assume that both nodes and components possess multi-state capacities and behave independently, enabling node-component equivalence transformations to simplify reliability computation. However, for practically relevant Binary-Node Multi-State Networks (BN-MSNs), where nodes operate in strictly binary states (normal/failed) and all component capacities fully depend on incident node, such transformations are no longer applicable. In BN-MSNs, any node failure forces immediate capacity loss for all adjacent components, significantly increasing modeling and computational complexity. To address this challenge, this paper proposes an extended modeling framework and an indirect reliability evaluation algorithm tailored for BN-MSNs. An enhanced capacity model is first developed to embed the "node failure induces component failure" dependency mechanism. Based on this model, network reliability is decomposed into reliabilities of subgraphs corresponding to all possible node-state combinations, and overall reliability is reconstructed via the law of total probability. To mitigate combinatorial explosion of node-state space, a pruning theorem for node-state combinations is established, effectively eliminating subgraphs that do not require further reliability analysis. Building upon this reduced search space, the method integrates multi-state minimal cut enumeration with probabilistic union computation to efficiently derive BN-MSN reliability. Experimental results demonstrate that the proposed method significantly reduces computational complexity versus traditional methods and consistently outperforms ablation benchmarks, validating the superior efficiency of integrated pruning and modeling strategies.

Keywords: Multi-state network (MSN), Binary-node multi-state network (BN-MSN), Node-component dependence, Multi-state minimal cut, Reliability evaluation algorithm..